System and method for a thermogravimetric analyzer having improved dynamic weight baseline

ABSTRACT

Systems and methods for minimizing extraneous forces and calculating corrected weights of samples based on buoyancy factors for a thermogravimetric analyzer (TGA). The TGA includes a balance chamber and a furnace configured to heat a sample. A null balance is provided in the balance chamber and is used to measure the sample weight change during heating. The furnace includes a cylinder open at the top to receive a sample. The bottom of the cylinder is closed except for a small hole that allows a thermocouple to pass through. An infrared heat source may be provided to heat the cylinder. The balance chamber can be thermally isolated from the furnace using an actively cooled plate and a system of heat shields disposed between the furnace and balance chamber. A thermocouple disk is further provided to limit gas flow in the furnace and increase reliability of sample weight measurements.

This application claims priority to U.S. Provisional Application No.60/639,301 filed Dec. 28, 2004 entitled System and Method for aThermogravimetric Analyzer Having Improved Dynamic Weight Baseline, andalso claims priority to and is a continuation of U.S. patent applicationSer. No. 11/317,050, filed Dec. 27, 2005, both of which are hereinincorporated by reference in their entirety

BACKGROUND

1. Field of the Invention

The present invention relates generally to improving weight measurementsof thermogravimetric analyzers. More particularly, the present inventionrelates to improving weight measurements for vertical thermogravimetricanalyzers with a balance positioned above the furnace.

2. Background of the Invention

Thermogravimetry is an analytical technique wherein a sample to beevaluated is subjected to a desired temperature program while its weightand temperature are measured. The weight change or the rate of weightchange with respect to time or temperature may be displayed as afunction of the measured temperature or of time and various evaluationsmay be performed. The weight curve versus temperature may be analyzed todetermine the magnitude of weight changes that occur and the temperatureor the range of temperatures at which they occur or other moresophisticated analyses may be performed such as those that determine thekinetics of the process responsible for the weight change.

A typical thermogravimetric analyzer (TGA) consists principally of asensitive balance to weigh the sample dynamically and a furnace to heatthe sample. TGAs are described, for example, in U.S. Pat. No. 5,165,792,which is incorporated by reference herein and attached as Exhibit 1.There are generally three configurations for TGAs: a horizontal furnace901 with a balance 903 alongside the furnace, as shown in FIG. 9A, avertical furnace 905 with the balance 903 below the furnace 905, asshown in FIG. 9B, or a vertical furnace 905 with the balance 903 abovethe furnace, as shown in FIG. 9C. In each of the configurations, a pan907 is connected to the balance 903 by a support 909. In principle, anytype of balance may be employed. However, the majority of TGAs use anull type balance that measures the force required to maintain thebalance in an equilibrium position. (An overview of the different typesof balances that may be employed in a TGA may be found in “Automatic andRecording Balances,” Saul Gordon and Clement Campbell, Anal. Chem. 32(5)271R-289R, 1960.)

A null balance comprises a drive system that applies force to thebalance movement that supports the sample pan and tare pan orcounterweight, a displacement sensor, and electronic control andmeasurement circuitry. These drive systems are typically electromagneticdrive systems. In operation, a force applied to the balance movement bythe drive system maintains the balance in the equilibrium, or nullposition. The force applied by the drive system to maintain the nullposition is a measure of the sample weight. Changes in sample weightcause the balance to be displaced from the equilibrium position, thedisplacement is sensed by the sensor and the balance movement isreturned to equilibrium by the drive system. Null balances are capableof sensing mass changes that are well below one microgram. Null balancesare also robust and relatively inexpensive.

When attempting to make high sensitivity weight measurements a number ofundesirable forces may act on the balance, sample, sample pan, andassociated components of the weighing system. (Some of these undesirableforces are described in Ultra Micro Weight Determination in ControlledEnvironments, S. P. Wolsky and E. J. Zdanuk eds., 1969, Interscience,39-46). For example, adsorption and desorption from the movingcomponents of the balance may cause spurious weight changes. Temperaturefluctuations within the balance may cause weight changes due to thermalexpansion of the balance arms or may affect the strength of the fielddeveloped by permanent magnets in electromagnetic drive systems soequipped. Static electric charges may collect and act on the balanceassembly, sample, and pan. Convection currents within the furnace orwithin the balance chamber may generate forces on the sample pan andassociated components. Buoyancy forces that vary with changes in gasdensity act on the sample and pan within the furnace. Radiometric forcesthat result from thermomolecular flow may act on the balance componentsin regions where temperature gradients exist. This particular problemmay be especially severe when operating under vacuum. The dynamic weightbaseline performance of a TGA depends critically on minimizing orcompensating for these undesirable forces or disturbances.

The dynamic weight baseline of a TGA is the weight measured when anexperiment is performed without a sample. In principle the dynamicweight measurement should be zero regardless of the temperature or theheating rate of the instrument. Deviations from zero are the result ofdisturbances acting on the balance assembly or pan. Given that a TGA isused to measure changes in weight that occur as a function oftemperature or time, any weight change that occurs in the absence of asample introduces uncertainty in the weight change measured during anexperiment when a sample is present.

The choice of TGA configuration can affect the degree to which theseextraneous forces act on the weight measurement. The horizontalconfiguration, as shown in FIG. 9A, is largely immune to convectioncurrents and thermomolecular forces because they act on the weighingsystem orthogonally to the gravitational force acting on the sample andthe balance. Horizontal systems, however, generally have much heavierbalance components that act to reduce sensitivity. This is because thesample and its pan must be supported by a cantilever beam structurecapable of resisting high temperatures within the furnace. The heavierstructure requires a more robust suspension that can also reduce thebalance sensitivity. Thermal expansion of the cantilever can materiallyaffect the weight measurement, and although in principle it can bereadily compensated for, thermal expansion remains a significantpotential source of weighing errors.

Vertically arranged TGAs may have the balance below or above thefurnace, as shown in FIGS. 9B and 9C. When the balance is below thefurnace, as shown in FIG. 9B, the structure that supports the sample panmust be relatively massive because it supports the pan in compressionand must resist the tendency to buckle, a tendency that is exacerbatedby the high temperatures that are often achieved in TGA. Like thehorizontal TGA, it requires a robust suspension and has relatively lowsensitivity. However, it is easier to isolate the balance thermally fromthe furnace because hot gas and effluent from the furnace tend to risebecause their temperature is high and density is low.

A TGA using a vertical furnace with the balance above it, as shown inFIG. 9C, offers the highest sensitivity because the mass of the pansuspension can be minimized, requiring only a fine filament to suspendthe pan. This allows the mass of the balance and its suspension to beminimized. However, thermal isolation is more difficult because of thetendency of hot gas and effluents to rise. A vertical TGA is moresusceptible to convection effects because of the orientation of thefurnace and the relatively large vertical thermal gradients thataccompany this configuration, and also because the thermomolecularforces act in parallel to the force of gravity and thus affect theweight measurement directly.

BRIEF SUMMARY OF THE INVENTION

The present invention relates to systems and methods for minimizingextraneous forces acting on the weighing system and calculatingcorrected weights of samples using buoyancy corrections. In an exemplaryembodiment, a TGA includes a balance chamber and a furnace configured toheat a sample. A null balance is provided in the balance chamber and isused to measure the weight of the sample as it changes with temperaturein the furnace. The furnace includes a cylinder that is open at the topto receive a sample. The bottom of the cylinder is closed except for asmall hole that allows a thermocouple to pass through.

The thermocouple is part of a thermocouple assembly arranged in thecylinder. The thermocouple assembly includes a thermocouple attached toa disk that is substantially the same diameter as an inner diameter ofthe cylinder. In operation, the thermocouple assembly is arranged belowthe sample to limit convective flows around the sample, which couldeffect the weight measurement of the sample.

The TGA also includes a water-cooled plate between the balance chamberand the furnace. This helps to thermally isolate the balance chamberfrom the furnace. By thermally isolating the balance chamber, thebalance temperature is kept constant, which eliminates weight errorsthat can result from thermal expansion of the balance beam and fromchanges in magnetic field strength due to changes of the magnettemperature. A thin metallic tube and system of heat shields are alsoused to isolate components of the balance from the heat of the furnace.

The TGA also includes a computer that can calculate a correction factorto be applied to the measured weight of the sample over varioustemperature ranges. The correction factors include a buoyancy factor forthe apparatus, a buoyancy factor for the sample, or both. Thiscorrection is determined for the particular gas surrounding the sample.Once the correction factor is calculated, it can be applied to themeasured sample weight to obtain a more accurate result.

In order to calculate a corrected sample weight, the TGA measures boththe sample weight via the balance and the temperature of the sample viathe thermocouple. Using these values, a correction factor, as describedabove, may be calculated and applied to the measured sample weight toget a corrected sample weight. In addition, in one embodiment of thepresent invention, a corrected temperature value is calculated that isused to determine the correction factor. This may be necessary, forexample, at the beginning of an experiment when the gas in the furnaceheats more quickly than the thermocouple, sample pan, and sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a TGA in accordance with anexemplary embodiment of the present invention.

FIG. 2 is a schematic of a front view of the TGA shown in FIG. 1.

FIG. 3 is a functional block diagram showing the operation of a nullbalance in accordance with the exemplary embodiment of the presentinvention.

FIG. 4 is a vertical cross section through the furnace assembly of theTGA shown in FIG. 1.

FIG. 5 is a horizontal cross section through the furnace assembly of theTGA shown in FIG. 1.

FIG. 6 is a vertical cross section through the balance chamber assemblyof the TGA shown in FIG. 1.

FIG. 7 is a flow chart showing a method of temperature and buoyancycorrection in accordance with an exemplary embodiment of the presentinvention.

FIG. 8 is a plot of a TGA dynamic weight baseline showing theuncorrected baseline and the baseline after buoyancy and temperaturemeasurement correction are applied in accordance with an exemplaryembodiment of the present invention.

FIGS. 9A, 9B, and 9C are schematics showing various known configurationsof TGAs.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to TGAs having an improved dynamic weightbaseline. In a preferred embodiment of the present invention, the TGAconfiguration is vertical, with the balance mounted above the furnace.This preferred configuration provides the highest weight sensitivity.

FIG. 1 is a schematic diagram of a TGA arranged in accordance with anexemplary embodiment of the present invention. TGA 100 includes abalance chamber 102, furnace 104, motorized linear actuator 106,electronic control unit 108, and TGA frame 110. Electronic control unit108 may include a computer that controls the operation of TGA 100 andreceives various measurements taken while TGA 100 is in use. Forexample, in one embodiment of the present invention control unit 108controls furnace movement and heating, operation of autosampler 116, andadditionally manipulates measurement data taken to determine parameterssuch as sample temperature and sample weight, as described furtherbelow. In another embodiment of the present invention, control unit 18can be configured to control operation of null balance 300.

A null balance 300 is arranged in balance chamber 102. Null balance 300will be described in greater detail below. Attached to null balance 300are suspension filaments (or “hang-down hooks”) 112 and 114. Hang-downhook 112 supports tare pan T, hang-down hook 114 supports samplematerial S in a pan (not shown). Each of hang-down hooks 112 and 114 areformed of slender filaments. An autosampler 116 may be used toautomatically load and unload sample materials in sample pans ontohang-down hook 114. It allows the TGA to perform a large number ofexperiments unattended. Autosampler 116 typically contains a traycapable of holding multiple sample pans and a mechanism for loading eachpan in its turn on hang-down hook 114.

FIG. 2 illustrates further details of system 100 according to oneembodiment of the present invention. Furnace 104 is attached to asupport structure 202 (shown in FIG. 2), which is attached to motorizedlinear actuator 106. Motorized linear actuator 106 and electroniccontrol unit 108 are mounted to TGA frame 110. Motorized linear actuator106 is electrically connected (not shown) to electronic control unit108. As shown in FIG. 1, furnace 104 is in the open position. In orderto close the furnace, linear actuator 106 is engaged and moves furnace104 upward to the closed position, as shown in FIG. 2.

An actively cooled plate 118 (see FIG. 2) located behind the indicatedsurface 118 a, is arranged between balance chamber 102 and furnace 104.In this “actively cooled plate” generally refers to a plate that removesheat by circulating fluid such as water, but could also be a Peltiercooled plate or similar device. In an embodiment of the presentinvention, plate 118 is temperature-controlled such that the platetemperature can be maintained at a relatively constant temperature.However, in other embodiments of the present invention, platetemperature need be controlled as long as active cooling takes place toprevent excessive heat buildup during operation of TGA 100 at elevatedtemperatures. An insulated cover 103 may be provided to protect thebalance chamber from atmospheric temperature fluctuations. Heaters (notshown) mounted on the balance chamber are used to control thetemperature of the balance chamber.

Referring again to FIG. 1, an interactive display 119 may be provided todisplay the results of any experiments run using TGA 100 as well as tocontrol operation of TGA 100.

FIG. 3 is a schematic diagram showing null balance 300 of the presentinvention. Null balance 300 consists of a horizontal balance beam (alsotermed “balance arm” herein) 310 having attachments at its extremitiesfor suspension of a sample pan (not shown) at one end and a tare pan(not shown) at the other end. The tare pan offsets the weight of thesample pan, thereby approximately balancing the sample pan mass andreducing the drive force required to maintain equilibrium. A metermovement 320 provides the drive force to maintain null balance 300 inthe null position and supports balance beam 310.

The meter movement 320 consists of a taut band (not shown) that supportsa wire coil 324 to which balance beam 310 is mounted and a fieldassembly comprising a permanent magnet 328 and magnetically soft ironarmature 329 to create a constant strength magnetic field. Electricalcurrent supplied by a meter coil drive 330 passes through wire coil 324and interacts with the magnetic field to apply torque to balance beam310 to maintain the null position. The electrical current in the coilwhen null balance 300 is in the null position is directly proportionalto the sum of the forces acting on balance arm 310 and is a measure ofthe sample weight when all of the extraneous forces have been eliminatedor accounted for.

Displacement of null balance 300 from the null position is sensed by adisplacement sensor that consists of a light emitting diode (LED) 342, apair of light sensing diodes 344, 346, a current source 348 toilluminate LED 342 and position error detection circuitry 349. A flag350 attached to balance beam 310 is interposed between LED 342 and lightsensing diodes 344, 346 such that flag 350 obscures a portion of thelight emitted by LED 342 toward sensing diodes 344, 346. Any movement offlag 350 changes the amount of light incident upon each of sensingdiodes 344, 346, increasing the energy reaching one and decreasing theenergy reaching the other.

The magnitude and sense of the imbalance of energy falling on sensingdiodes 344, 346 generates a position error signal that is fed to metercoil drive 330 that varies the coil current to restore null balance 300to the null position. Thus, the meter drive coil current is proportionalto the measured sample weight. To achieve optimum performance, anyextraneous forces acting on null balance 300 must be eliminated orcompensated, to eliminate or minimize errors in the measured weight.

FIGS. 4 and 5 illustrate exemplary features of a preferred embodiment ofthe present invention, wherein furnace 104 is an infrared furnace thatuses quartz halogen lamps. Four tubular quartz halogen lamps 510 (FIG.5) irradiate a silicon carbide cylinder 420 enclosed within a quartztube 430. Water-cooled reflector assembly 440 surrounds the four lamps510 and quartz tube 430 to direct the radiation emitted from lamps 510toward the outside surface of silicon carbide cylinder 420. Theradiation heats silicon carbide cylinder 420, which, in turn, heats thesample (not shown), sample pan 450 and thermocouple disk 460 locatedwithin silicon carbide cylinder 420. Silicon carbide was chosen becauseit is capable of resisting the high temperatures encountered in a TGA,has high thermal conductivity that improves temperature uniformity andhas high emissivity so that it heats efficiently. Lower end 422 of thesilicon carbide cylinder is closed except for a small hole 424 for asupport for thermocouple disk 460, while top end 426 of cylinder 420 isopen to allow the sample pan 450 to enter furnace 104.

The temperature inside cylinder 420 is measured by a thermocouple (notshown) welded to thermocouple disk 460, which is nearly the samediameter as the inside of the silicon carbide cylinder 420 and locatedjust below sample pan 450. This configuration leads to improvedtemperature uniformity that helps to reduce temperature gradients in theregion of sample pan 450, which reduces gas density differences withinthis region and hence reduces gas circulation by natural convection thatmay cause weighing errors. It also restricts the effective size offurnace 104 immediately surrounding and below sample pan 450 to limitthe circulation of gas resulting from density differences caused bynon-uniformity of temperature within the furnace 104.

Purge gas enters furnace 104 via inlet tube 470, passes through hole 428of the vertical wall of silicon carbide cylinder 420. The purge gaspasses above the sample in sample pan 450 and exits via a second hole429 through the vertical wall of silicon carbide cylinder 420 locateddiametrically opposite first hole 428. The purge gas exits furnace 104via exit tube 480. Typical purge gases include dry air, oxygen,nitrogen, argon, helium, carbon monoxide and carbon dioxide.

Because the flow of purge gas from inlet 470 to exit 480 is orthogonalto the force of gravity, it has a minimal effect on the weightmeasurement. Thus it will be recognized that a furnace having thisconfiguration will greatly reduce gas flow forces acting on sample pan450, whether the flows are from purge gas or result from densitydifferences due to temperature variation within the furnace.

FIG. 5 is a horizontal cross section through the furnace assembly takenat the centerline of purge gas inlet tube 470 and exit tube 480. Quartztube 430 is located at the center of reflector 440 and is surrounded byfour tubular quartz halogen lamps 510 disposed equidistant from thequartz tube and from one another. Cavity 541 of the reflector, which isthe reflecting surface, is formed by the intersection of four ellipticalcylinders. Each cylinder is disposed such that one of its foci iscoincident with the centerline of the quartz tube and its other focus iscoincident with the centerline of the lamp within that cylinder. In thisfashion, the majority of the radiation emitted by the lamps is directedtoward the silicon carbide cylinder at the center of the quartz tube.

FIG. 6 illustrates further details of a null balance chamber, accordingto one embodiment of the present invention, Null balance 300 with asuspension filament pan support 114 is arranged in a temperaturecontrolled balance chamber 102, as shown in FIG. 6. As shown in FIG. 1,balance chamber 102 is mounted above furnace 104. Preferably, balancechamber 102 has its temperature precisely controlled above ambienttemperature and is thermally isolated from its surroundings, inparticular from furnace 104 disposed beneath it. Thermal isolation ofbalance chamber 102 is accomplished using thermal insulation surroundingthe chamber (not shown) and structural supports 610 and 612 that havehigh thermal resistance while possessing high rigidity. Thermalisolation of balance chamber 102 from furnace 104 is additionallyachieved by placing actively cooled plate 118 beneath balance chamber102. Suspension filament 114 passes through water-cooled plate 118.Water-cooled plate 118 supports a thin wall metallic tube 620 and asystem of heat shields 630 attached to the bottom of tube 620. Metallictube 620 shields suspension filament 114. Water-cooled plate 118, thinmetallic tube 620 and heat shields 630 are grounded to facilitatedischarge of static charges.

In operation, furnace 104 is lowered to load a sample. When furnace 104is raised to run an experiment, it closes against water-cooled plate118. Heat shields 630 attached to thin metallic tube 620 enter furnace104 and are located above the open end 426 of silicon carbide cylinder420 when furnace 104 is fully raised. In this manner, balance chamber102 is thermally isolated from furnace 104.

Null balance 300 contains a substantially small amount of hygroscopicmaterial (such as polymeric materials and adhesives) and balance chamber102 is purged with dry gas to reduce the magnitude of moistureadsorption. To eliminate the accumulation of static charge, balance beam310 and suspension filament 114 are entirely made of metal and areelectrically grounded by a fine gauge spring wire (not shown) so thatstatic charges will be readily discharged to ground.

To obtain high precision weight measurements in TGA, buoyancycorrections must be applied to the measured weight. The buoyancycorrection is based upon the Archimedes principle that a buoyancy forceacts on an immersed body that is equal to the weight of the displacedfluid. Because the temperature of the gas within furnace 104 (and henceits density) changes during an experiment, the buoyancy force changes.Gas density decreases with increasing temperature so that the buoyancyforce decreases and an apparent weight gain is observed. Two componentsof buoyancy force may be included, one attributable to the apparatus andthe other attributable to the sample. The apparatus component hasessentially constant volume, neglecting changes in volume due to thermalexpansion and includes sample pan 450 and a portion of pan suspensionfilament 114. The sample component has variable volume due to weightloss. The buoyancy correction equations A and B are based on the idealgas law (Eq. C) and assume that the gas pressure is constant Thus gasdensity is inversely proportional to absolute gas temperature.

Apparatus Buoyancy Force Correction

$\begin{matrix}{b_{a} = {V_{a}{\rho_{i}\left( {1 - \frac{T_{t}}{T}} \right)}}} & \left\lbrack {{Eq}.\mspace{14mu} A} \right\rbrack\end{matrix}$

Sample Buoyancy Force Correction

$\begin{matrix}{b_{s} = {V_{i}\frac{m_{s}}{m_{i}}{\rho_{i}\left( {1 - \frac{T_{i}}{T}} \right)}}} & \left\lbrack {{Eq}.\mspace{14mu} B} \right\rbrack\end{matrix}$

Gas Density Equation (Ideal Gas Law)

$\begin{matrix}{\rho = \frac{p}{RT}} & \left\lbrack {{Eq}.\mspace{14mu} C} \right\rbrack\end{matrix}$

The gas density equation is used to calculate the densities used in theapparatus and sample buoyancy force equations, or tabular data may beused. The corrected weight measurement is then determined by subtractingfrom the measured sample weight both the apparatus and sample buoyancyfactors.

Corrected Weight Measurement

m=m _(s) −b _(s) −b _(a)  [Eq. D]

The following definitions are provided for the above equations:

-   -   b_(a)—apparatus buoyancy correction to the weight measurement    -   V_(a)—apparatus volume, that of the pan and a portion of the pan        suspension filament    -   ρ_(t)—density of the gas when the pan weight is tared    -   T_(t)—absolute temperature of the gas when the pan weight is        tared    -   T—absolute temperature of the gas during the experiment    -   b_(s)—sample buoyancy correction to the weight measurement    -   V_(i)—volume of the sample when the starting sample weight is        measured    -   m_(s)—measured sample weight (initial pan mass is tared)    -   m_(i)—initial sample weight    -   ρ_(i)—density of the gas when the initial sample weight is taken    -   T_(i)—absolute temperature of the gas when the initial sample        weight is taken    -   p—atmospheric pressure (assumed to be 101300 Pa)    -   R—specific gas constant

Sample and pan buoyancy corrections are applied to the TGA weightmeasurement using the measured temperature to calculate the buoyancyforce to be subtracted from the weight measurement. Start-up weightoffsets occur because the gas in furnace 104 heats more quickly thansample pan 450, sample and thermocouple disk 460. Thus, adisproportionately large buoyancy force occurs at low temperature thatis not properly compensated by the buoyancy correction. A temperaturecorrection may be applied to the measured temperature to reduce thestart-up weight gain. Assuming the temperature of the gas is close tothat of silicon carbide cylinder 420 and that heat exchange betweenthermocouple disk 460 and cylinder 420 is predominately by diffuse-grayradiation, a simple expression for cylinder 420 and gas temperature maybe used for temperature correction.

Temperature Correction

$\begin{matrix}{T = \left( {{K_{m}{\overset{.}{T}}_{m}} + T_{m}^{4}} \right)^{\frac{1}{4}}} & \left\lbrack {{Eq}.\mspace{14mu} E} \right\rbrack\end{matrix}$

The following definitions are provided for the above equation:

-   -   T_(m)—measured absolute temperature (T_(m) with a dot indicates        a time derivative, i.e., dT_(m)/dt, where t represents time)    -   T—cylinder absolute temperature    -   K_(m)—empirical heat exchange coefficient

When the temperature correction is employed, the value of T calculatedabove is substituted for the temperature in the buoyancy correctionequations; otherwise the temperature measured by the thermocouple isused without the correction.

In preferred embodiments of the present invention, algorithms based onthe above equations A-E or mathematical equivalents thereof, areperformed by processor 108 in order to properly calculate sample weightand sample temperature. The term “mathematical equivalents” refers toequations or algorithms that operate to produce the same result based ongiven input and variables. Thus, one algorithm that is the mathematicalequivalent of equation D above would be: a) summing up the buoyancycorrection factors b_(a) and b_(s)) subtracting the result from measuredsample weight m_(s) to obtain m, in other words m=m_(s)−(b_(s)+b_(a)).

FIG. 7 is a flowchart showing exemplary steps and inputs involved in amethod of correcting the TGA weight measurement for buoyancy effects,according to an embodiment of the present invention. Preferably,electronic control unit 108 is configured to perform the TGA weightmeasurement correction steps outlined in FIG. 7. Temperature andbuoyancy corrections performed in steps 714, 716, 718, and 722 are basedon equations E, B, A, and D, respectively, or their mathematicalequivalents. Inputs 710, 720 are the measured temperature from athermocouple situated within the silicon carbide cylinder beneath thesample pan and the sample weight measured by the null balance,respectively. Output 730 is the measured weight corrected for buoyancyeffects.

At step 712, the measured temperature T_(m) supplied at input 710 may beleft uncorrected, in which case the method moves to steps 716 and 718described below. Alternatively, if it is determined that the measuredtemperature T_(m) is to be corrected, the method moves to step 714 wherethe temperature correction as described above in Eq. E is applied, andsubsequently the corrected temperature value is supplied as theparameter T for the buoyancy correction operations performed at steps716 and 718.

Steps 716 and 718 receive as temperature input, either the value T_(m)directly supplied from input 710 through step 712, or the value T,supplied from step 714. In addition to a temperature input, measuredweight m_(s) is supplied from input 720 to the sample buoyancycorrection calculation performed at step 716, which, along with the gastemperature T (either calculated T from step 714 or T_(m) from input710), is used to calculate the sample buoyancy force b_(s). Gastemperature T (using calculated T from step 714 or T_(m) from input 710)is the sole input used to calculate the apparatus buoyancy correctionb_(a) at step 718.

In step 722, correction factors, if any, are applied to the measuredsample weight m_(s) to determine the corrected sample weight m. In theexample depicted in FIG. 7, the sample and apparatus buoyancy forcesb_(s) and b_(a), respectively, are subtracted from the sample weight atstep 722 to give the buoyancy corrected weight m supplied as output 730.However, in other embodiments of the present invention, the user of theTGA may chose to apply b_(s) alone, b_(a) alone, or neither of thebuoyancy corrections in determining m.

Additionally, the user may also choose on an individual sample basis aswhether to apply the gas temperature correction of Eq. E. Theexperimental method outlined in FIG. 7 can be repeated for any number oftemperature measurements and can be programmed to follow a specifictemperature profile (a specific protocol including a temperature rangeor set of temperature ranges for sample heating, heating rate or ratescorresponding to the temperature ranges, hold temperatures and holdtimes, if any, etc.). In this manner, a buoyancy corrected sample weightcan be determined and stored as a function of temperature over anydesired accessible temperature range and temperature profile.

FIG. 8 shows the dynamic weight baseline result for a TGA constructedaccording to the present invention with and without the buoyancycorrection described herein. The TGA was heated between 50° C. and 1200°C. at 20° C./min with an empty pan installed. The result labeled 810shows the resulting weight signal in micrograms without buoyancycorrection. In principle, the weight gain should be negligible duringthis experiment. However, there are two significant weight gains to notein curve 810. First, at the initiation of heating from the startingtemperature of 50° C., the weight increases by approximately 3 μg almostimmediately. This is the start-up buoyancy effect that is the result ofthe gas within the furnace heating faster than the pan and thermocouple.The second effect is the gradual increase in weight throughout theremainder of the experiment. Both effects are the result of reducedbuoyancy force acting on the pan as the gas temperature rises.Altogether, there is an apparent weight gain of 17.4 μg. This amount ofweight gain can accordingly by considered to be mostly an artifact ofthe TGA measurement and not any true sample weight gain. The resultlabeled 820 is the buoyancy corrected dynamic baseline determinedaccording to the methods of the present invention described above. Theprompt start-up weight gain is greatly reduced, while the total apparentweight gain is reduced to 4.5 μg by the application of the buoyancycorrection. Thus, the vast majority of the sample weight gain artifactsare eliminated. In addition, because embodiments of the presentinvention serve to reduce artifacts such as balance chamber temperaturefluctuations, static charge buildup, and sample furnace convectioncurrents, each of which can cause unpredictable changes in apparentsample weight, when TGA measurements are recorded with buoyancy andtemperature corrections applied, the resulting dynamically correctedcurves yield much more reproducible results for any given sample.Additionally, less variation in TGA measurements is seen betweenmeasurements performed on different instruments that employ theembodiments of the present invention disclosed above.

The foregoing disclosure of an exemplary embodiment of the presentinvention has been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise forms disclosed. Many variations andmodifications of the embodiments described herein will be apparent toone of ordinary skill in the art in light of the above disclosure. Thescope of the invention is to be defined only by the claims appendedhereto, and by their equivalents.

Further, in describing representative embodiments of the presentinvention, the specification may have presented the method and/orprocess of the present invention as a particular sequence of steps.However, to the extent that the method or process does not rely on theparticular order of steps set forth herein, the method or process shouldnot be limited to the particular sequence of steps described. As one ofordinary skill in the art would appreciate, other sequences of steps maybe possible. Therefore, the particular order of the steps set forth inthe specification should not be construed as limitations on the claims.In addition, the claims directed to the method and/or process of thepresent invention should not be limited to the performance of theirsteps in the order written, and one skilled in the art can readilyappreciate that the sequences may be varied and still remain within thespirit and scope of the present invention.

1. A thermogravimetric analyzer comprising: (a) a balance chambercontaining a null balance; (b) a vertical furnace containing an infraredheat source configured to heat a cylinder contained therein, thecylinder adapted to transfer heat to the sample; (c) an actively cooledplate positioned between the balance chamber and the furnace, whereinthe actively cooled plate is one of a Peltier-cooled plate, awater-cooled plate, and a plate cooled by liquid; (d) a filamentconnected to the null balance; and (e) a sample pan supported by thefilament in the furnace and configured to support a sample.
 2. Thethermogravimetric analyzer of claim 1, wherein the liquid is water. 3.The thermogravimetric analyzer of claim 1, further comprising: (a)further comprising a thin metallic tube enclosing the filament; and (b)a plurality of heat shields supported by the thin metallic tube anddisposed between the balance chamber and the furnace.
 4. Thethermogravimetric analyzer of claim 1, wherein the actively cooled plateis configured to improve thermal isolation of the balance chamber byremoving heat received from the furnace.
 5. The thermogravimetricanalyzer according to claim 1, wherein the infrared heat source is aplurality of halogen lamps.
 6. The thermogravimetric analyzer accordingto claim 1, further comprising: (a) an insulated cover surrounding thebalance chamber; and (b) heaters mounted on the balance chamber, andadapted to control temperature of the balance chamber.
 7. Thethermogravimetric analyzer according to claim 1, further comprising aprocessor configured to receive from the balance a corresponding valueof measured weight m_(s) of a sample placed on the sample pan, theprocessor further configured to calculate a buoyancy correction factorto be applied to m_(s) to determine a corrected weight m, wherein thebuoyancy correction factor includes one or more of a sample buoyancycorrection factor b_(s) and a sample pan and filament buoyancycorrection factor b_(a), wherein m is calculated by one of:m=m _(s) −b _(s) −b _(a) or a mathematical equivalent;  1)m=m _(s) −b _(s) or a mathematical equivalent; and  2)m=m _(s) −b _(a) or a mathematical equivalent.  3)
 8. Thethermogravimetric analyzer according to claim 6, wherein b_(s) is givenby:$b_{s} = {V_{i}\frac{m_{s}}{m_{i}}{\rho_{i}\left( {1 - \frac{T_{i}}{T}} \right)}}$or a mathematical equivalent, and wherein b_(a) is given by$b_{a} = {V_{a}{\rho_{i}\left( {1 - \frac{T_{t}}{T}} \right)}}$ or amathematical equivalent, where: V_(a) is an apparatus volume, that ofthe pan and a portion of the pan filament, ρ_(t) is density of gas inthe sample chamber when sample pan weight is tared, T_(t) is absolutetemperature of the gas when sample pan weight is tared, T is absolutetemperature of the gas corresponding to each received sample weightmeasurement, V_(i) is a volume of the sample when the initial sampleweight is measured, m_(i) is initial sample weight, ρ₁ is density of thegas when the initial sample weight is measured, and T_(i) is absolutetemperature of the gas when the initial sample weight is measured.
 9. Athermogravimetric analyzer comprising. (a) a balance configured toperiodically measure sample weight over a temperature range; (b) afurnace containing an infrared heat source configured to heat a cylindercontained therein, the cylinder adapted to transfer heat to the sample;(c) a pan supporting the sample; (d) a filament connecting the pan tothe balance, the pan and a portion of the filament being located withinthe cylinder; (e) a thermocouple located inside the cylinder, thethermocouple being welded to a disk of substantially the same diameteras an inner diameter of the cylinder and arranged beneath the pan suchthat the disk restricts circulation of gas caused by differences oftemperature within the cylinder; (f) a balance chamber disposed abovethe furnace and configured to contain the balance therein and tothermally isolate the balance from the furnace; and (g) an activelycooled plate positioned between the balance chamber and the furnace,wherein the actively cooled plate is one of a Peltier-cooled plate, awater-cooled plate, and a plate cooled by a liquid.
 10. Thethermogravimetric analyzer according to claim 9, further comprising acomputer configured to calculate a correction factor to be applied tothe sample weight measured by the balance over the temperature range.11. The thermogravimetric analyzer according to claim 9, wherein thebalance is a null balance.
 12. The thermogravimetric analyzer accordingto claim 11, wherein the null balance comprises a balance arm configuredto support the pan, a drive system configured to apply force to thebalance arm, a displacement sensor configured to detect displacement ofthe balance arm, and control means configured to operate the drivesystem to keep the balance arm in equilibrium.
 13. The thermogravimetricanalyzer according to claim 11, wherein the computer is configured toreceive an output from the drive system measuring the force applied bythe drive system to keep the balance arm in equilibrium and furtherconfigured to convert the output to a measured weight of the sample. 14.The thermogravimetric analyzer according to claim 11, wherein thecylinder includes a first hole configured to allow transmission of apurge gas into the cylinder and a second hole configured to allowtransmission of the purge gas out of the cylinder, wherein each hole islocated on a vertical wall of the cylinder.
 15. A thermogravimetricanalyzer comprising: (a) a balance; (b) a pan for supporting a sample;(c) a filament connecting the pan to the balance; (d) a furnace to heatthe sample; (e) means for measuring a weight m_(s) of the sample; and(f) means for calculating a corrected weight m, using a buoyancycorrection factor, wherein the buoyancy correction factor includes oneor more of a sample buoyancy correction factor b_(s) and a sample panand filament buoyancy correction factor b_(a), wherein m is calculatedby one of:m=m _(s) −b _(s) −b _(a) or a mathematical equivalent;  1)m=m _(s) −b _(s) or a mathematical equivalent; and  2)m=m _(s) −b _(a) or a mathematical equivalent.  3)
 16. Thethermogravimetric analyzer according to claim 15, wherein b_(s) is givenby:$b_{s} = {V_{i}\frac{m_{s}}{m_{i}}{\rho_{i}\left( {1 - \frac{T_{i}}{T}} \right)}}$or a mathematical equivalent, and wherein b_(a) is given by$b_{a} = {V_{a}{\rho_{i}\left( {1 - \frac{T_{t}}{T}} \right)}}$ or amathematical equivalent, where: V_(a) is an apparatus volume, that ofthe pan and a portion of the pan filament, ρ_(t) is density of gas inthe sample chamber when sample pan weight is tared, T_(t) is absolutetemperature of the gas when sample pan weight is tared, T is absolutetemperature of the gas corresponding to each received sample weightmeasurement, V_(i) is a volume of the sample when a starting sampleweight is measured, m_(i) is initial sample weight, ρ_(i) is density ofthe gas when the initial sample weight is measured, and T_(i) isabsolute temperature of the gas when the initial sample weight ismeasured.
 17. The thermogravimetric analyzer according to claim 15,further comprising a thin metallic tube surrounding the filament andhaving attached heat shields, wherein the furnace is a vertical furnace,and wherein the balance is a null balance.
 18. The thermogravimetricanalyzer according to claim 17, wherein the furnace is configured toheat a cylinder contained therein, the cylinder adapted to transfer heatto the sample, wherein the cylinder includes a first hole configured toallow transmission of a purge gas into the cylinder and a second holeconfigured to allow transmission of the purge gas out of the cylinder,wherein each hole is located on a vertical wall of the cylinder
 19. Thethermogravimetric analyzer according to claim 17, wherein the nullbalance comprises a balance arm configured to support the pan, a drivesystem configured to apply force to the balance arm, a displacementsensor configured to detect displacement of the balance arm, and controlmeans configured to operate the drive system to keep the balance arm inequilibrium.
 20. The thermogravimetric analyzer according to claim 15,wherein the means for measuring the weight of the sample comprisesmeasuring the force applied by the drive system to keep the balance armin equilibrium.
 21. The method according to claim 20, wherein step (b)further comprises compensating for low temperature at start-up bysubstituting for T based on a measured temperature T_(m) according to:$T = \left( {{K_{m}{\overset{.}{T}}_{m}} + T_{m}^{4}} \right)^{\frac{1}{4}}$or a mathematical equivalent, wherein K_(m) is an empirical heatexchange coefficient.